Question: What do the following two equations represent? $2x+5y = 5$ $-6x-15y = 1$
Solution: Putting the first equation in $y = mx + b$ form gives: $2x+5y = 5$ $5y = -2x+5$ $y = -\dfrac{2}{5}x + 1$ Putting the second equation in $y = mx + b$ form gives: $-6x-15y = 1$ $-15y = 6x+1$ $y = -\dfrac{2}{5}x - \dfrac{1}{15}$ The slopes are equal, and the y-intercepts are different, so the lines are parallel.